Field probe isotropic compensation using orthogonal scalar field components

ABSTRACT

A method, system and apparatus for compensating for non-ideal isotropic behavior of a field probe are disclosed. A method includes, during a calibration procedure, for each of a plurality of positions of the field probe relative to a source, each position denoted by a set of angles (θ, ϕ), performing the following steps: measuring a field by the sensors of the probe, storing the measurements and the set of angles (θ, ϕ) for each measurement, computing a correction factor for the set of angles (θ, ϕ) based on the measurement, and storing the correction factors. During a measurement procedure, each sensor measures a component of the field. A set of angles is determined based on the sensor measurements, and a correction factor is determined based on the set of angles. The correction factor may then be multiplied by the sensor measurements to obtain the corrected field measurements.

FIELD

The present disclosure relates to wireless communications, and inparticular, to implementation of field probe isotropic compensationusing orthogonal scalar field components.

INTRODUCTION

Isotropic field probes are used widely in electromagnetic fieldmeasurements. For example, electric field probes are used in radiatedimmunity (RI) measurements for electromagnetic compatibility (EMC)testing. A feature of the probes is their isotropic behavior. The fieldprobe should report the same reading regardless of the direction of theincident field. This may be achieved by using three orthogonallyoriented dipole or monopole sensing elements or antennas. Some designsuse more sensing elements for improved sensing of an incident field fromdifferent directions. For example, some designs use six monopoleorthogonal sensors in x+, x−, y+, y−, z+ and z− directions. FIG. 1 showsan example of an electric field probe 10 having three orthogonal sensors12 x, 12 y and 12 z. The probe can be thought of as being situated atthe corner of an imaginary cube.

The three orthogonally oriented elements of FIG. 1 are denoted as x, yand z sensors. Each of the sensors is linearly polarized, and measuresthe electric field parallel to the sensor polarization direction. Thetotal electric field is calculated by:

E _(total)=,√{square root over (E _(x) ² +E _(y) ² +E _(z) ²)}  (1)

where E_(total) is the total electric field measured by the probe.E_(x), E_(y), E_(z) are the electric field for x, y and z polarizations,respectively. For electrically small dipole and monopole sensorelements, each of the antenna patterns is similar to that of a pointdipole. In such a case, the field probe is isotropic, i.e., the totalelectric field E_(total) measured by the probe is the same regardless ofthe incident field directions. This can be illustrated by the exampleshown below.

Assume an incident plane wave with the E field polarized in the xdirection. As the probe rotates from 0 degrees to 360 degrees about thex-axis, the electric field reading from the three sensors is recorded.

The responses from the three sensors as a function of the rotation angleare shown in FIG. 2. The total electric field when summed using Eq. (1)is constant as shown by the horizontal line at the value 1 on thevertical axis. It is evident that the summed response of the probe isnot a function of the orientation of the probe with respect to thedirection of the incident field. Even though the description above usesan x-oriented incident field for illustration, the field orientation isnot limited. It can be shown that the probe response is isotropic evenwhen the incident field direction is arbitrary. This is valid when eachof the sensors possesses a radiation pattern similar to a point dipole.

The field probes may be designed to be broadband devices. For example,the field probe shown in FIG. 1 may have a specified frequency rangefrom 100 KHz to 6 GHz. At higher frequencies, for example, at greaterthan 3 GHz for such a probe, the sensors 12 x, 12 y and 12 z becomeelectrically large, and the radiation patterns of the sensors deviatefrom that of a point dipole. As a result, the isotropic response of theprobe deteriorates. In some cases, several dB of variations from theideal isotropic behavior can be seen.

FIG. 3 shows an example of a probe rotational response about theorthogonal angle where each sensor has higher gain than a point dipole.This is typical of a probe at the higher end of the frequency range ofoperation of the probe. It is seen that the probe is no longer perfectlyisotropic resulting in substantial fluctuation of the total electricfield as a function of angle.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments, and theattendant advantages and features thereof, will be more readilyunderstood by reference to the following detailed description whenconsidered in conjunction with the accompanying drawings wherein:

FIG. 1 illustrates an orientation of a 3-axis field probe having threesensors;

FIG. 2 shows responses from the three sensors as a function of therotation angle;

FIG. 3 shows an example of a probe rotational response about theorthogonal angle where each sensor has higher gain than a point dipole;

FIG. 4 is a flowchart of an exemplary process during a calibrationprocedure for measuring and storing field measurements, angles andcorrection factors for a field probe;

FIG. 5 is a flowchart of an exemplary process during a measurementprocedure for correcting a measured field by a correction factor;

FIG. 6 is a flowchart of an exemplary process during a calibrationprocedure for measuring and storing field measurements, angles andcorrection factors for a field probe; and

FIG. 7 is a flowchart of an exemplary process during a measurementprocedure for correcting a measured field by a correction factor; and

FIG. 8 is a block diagram of calibration and measurement correctionprocessing circuitry according to principles set forth herein.

DETAILED DESCRIPTION

Before describing in detail exemplary embodiments, it is noted that theembodiments reside primarily in combinations of apparatus components andprocessing steps related to implementation of field probe isotropiccompensation using measured scalar field components. Accordingly,components have been represented where appropriate by conventionalsymbols in the drawings, showing only those specific details that arepertinent to understanding the embodiments so as not to obscure thedisclosure with details that will be readily apparent to those ofordinary skill in the art having the benefit of the description herein.Like numbers refer to like elements throughout the description.

As used herein, relational terms, such as “first” and “second,” “top”and “bottom,” and the like, may be used solely to distinguish one entityor element from another entity or element without necessarily requiringor implying any physical or logical relationship or order between suchentities or elements. The terminology used herein is for the purpose ofdescribing particular embodiments only and is not intended to belimiting of the concepts described herein. As used herein, the singularforms “a”, “an” and “the” are intended to include the plural forms aswell, unless the context clearly indicates otherwise. It will be furtherunderstood that the terms “comprises,” “comprising,” “includes” and/or“including” when used herein, specify the presence of stated features,integers, steps, operations, elements, and/or components, but do notpreclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

In embodiments described herein, the joining term, “in communicationwith” and the like, may be used to indicate electrical or datacommunication, which may be accomplished by physical contact, induction,electromagnetic radiation, radio signaling, infrared signaling oroptical signaling, for example. One having ordinary skill in the artwill appreciate that multiple components may interoperate andmodifications and variations are possible of achieving the electricaland data communication.

In some embodiments described herein, the term “coupled,” “connected,”and the like, may be used herein to indicate a connection, although notnecessarily directly, and may include wired and/or wireless connections.

Some embodiments provide a post processing algorithm as described hereinto compensate for the non-ideal isotropic behavior of the probes. Forexample, for the probe having a response as shown in FIG. 3, assume theprobe is placed in a field with an unknown incident direction. Suppose,for example, that the probe reading (Ex, Ey, Ez) is (0.5, 0.5, 0) afternormalizing to the maximum reading. From FIG. 3, for the probe to readwith the same amplitude in the x, y, and z directions, the incidentfield angle should be 60 degrees. It is then possible to estimate theangle of incidence. Once the angle of incidence is known, the proberesponse as a function of angle can be corrected.

In a 3-dimensional sense, probe pattern corrections work similarly. The3D radiation patterns of the probe may be characterized first. Forexample, this can be measured during the calibration or design of theprobe by rotating the probe in three dimensions, for example using a (θ,ϕ) positioner. A 3D map may then be established for Ex, Ey and Ez at anyincident angle, i.e., for each (θ, ϕ) pair, there is a corresponding(Ex, Ey, Ez) reading by the probe, or in the case of six orthogonalsensors, a corresponding (Ex+, Ex−, Ey+, Ey−, Ez+, Ez−) reading. In someembodiments, the six orthogonal sensors may be grouped by orthogonalpairs of sensors, each sensor in a pair being opposite in direction sothat, for example, a first pair of sensors measure Ex+ and Ex− and are180 degrees apart−, a second pair of sensors measure Ey+ and Ey− and are180 degrees apart, and a third pair of sensors measure Ez+ and Ez− andare 180 degrees apart. In some embodiments, the average value of Ex+ andEx−, for example, measured at a point may be taken as the value of Ex atthe point. In some embodiments, the maximum of Ex+ and Ex−, for example,may be taken as the value of Ex at the point. The same holds true for Eyand Ez. Results can be extended to other probes having sensors in fewerthan or more than three or six dimensions.

This data may then be used in a lookup table when the probe is immersedin a wave with unknown orientation to determine the direction of thefield. A correction factor can be computed for each incident direction(θ, ϕ). In other words, the correction factor k may be calculated as

$\begin{matrix}\begin{matrix}{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}} & \;\end{matrix} & (2)\end{matrix}$

where k is the isotropic correction factor for incident field angle (θ,ϕ), and E_(inc) is the known magnitude of the applied field whenmeasuring the 3D pattern.

When a measurement is done using the probe, the probe reading may firstbe normalized, e.g., (E_(x)/√{square root over (E_(x) ²+E_(y) ²+E_(z)²)}, E_(y)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(z)/√{squareroot over (E_(x) ²+E_(y) ²+E_(z) ²)}). This normalized reading may thenbe used to find the set of angles corresponding to this reading from thetable of angles. There could be multiple angle pairs (θ, ϕ) which canpotentially match the probe reading. This is not of concern forisotropic compensation purposes for they may have the same correctionfactor k (θ, ϕ).

From the probe readings of the 3-axes E field information, it ispossible to estimate the angle of arrival of the incident field. Analgorithm may be used to estimate the angle. In some embodiments, theestimated angle is the angle in a table that corresponds to the measuredE field information. Correction factors for an isotropic response can beapplied from a previously characterized 3D probe pattern. The correctionfactor to be applied is a correction factor that corresponds to theestimated angle and is stored in the table. Once the correction factoris obtained for the estimated angle, the measured E field informationmay be multiplied by the correction factor to correct for the anisotropyof the field probe.

Thus, even when the underlying probe response is not entirely isotropic,full isotropy may be achieved with some of the methods set forth herein.

FIG. 4 is a flowchart of an exemplary process for compensating fornon-ideal isotropic behavior of a field probe. The process includes,during a calibration procedure, for each of a plurality of positions ofthe field probe relative to a source, each position denoted by a set ofangles, performing the following steps (Block S100): measuring a fieldby a plurality of sensors of the field probe and store the measurementand the set of angles for the measurement (Block S102); and computing acorrection factor for the set of angles based on the measurement andstore the correction factor (Block S104).

Ideally, suppose the probe should measures, after normalization, 1.0 onthe x-axis sensor, zero on the y-axis sensor and zero on the z-axissensor. Suppose the actual measurement is (0.8, 0.2, 0.3). Then thecorrection factor should be k(θ, ϕ)=1.1396, and this correction factorwould be stored for the angle (0, 0).

The process further includes, for each position of the probe, storingthe field probe readings, the angles and the correction factor for eachset of angles (block S104).

FIG. 5 is a flowchart of an exemplary process for compensating fornon-ideal isotropic behavior of a field probe is provided. The processincludes, during a measurement procedure (Block S106), measuring a fieldby a plurality of sensors of the field probe (Block S108). The processalso includes using the measurement to determine an angle of incidence(Block S110). The process also includes determining a correction factorcorresponding to the angle of incidence (Block S112). The process alsoincludes multiplying the measured field by the correction factor toobtain a corrected measurement (Block S114). Suppose that the x, y and zmeasurements are (0.8, 0.2, 0.3) and suppose that the magnitude of theincident field is 1. This ordered triplet is looked up in the table andthe angle (0, 0) is retrieved. For this angle, the correction factork(θ, ϕ) equal to 1.1396 is retrieved and this correction factor is aremultiplied by the measurements Ex, Ey and Ez to achieve a correctedfield Ex, Ey, and Ez.

FIG. 6 is a flowchart of an exemplary process for compensating fornon-ideal isotropic behavior of a field probe having at least threeorthogonal sensors. The process includes during a calibration procedure,for each of a plurality of positions of the field probe relative to asource, each position denoted by a set of angles, performing thefollowing steps (Block S116). The process includes obtaining ameasurement by each sensor (Block S118). The process also includescomputing a correction factor, k for each set of angles based on themeasurements (Block S120). The process further includes storing eachmeasurement, storing the set of angles corresponding to the measurementsand storing the correction factor k for the set of angles (Block S122).

FIG. 7 is a flowchart of an exemplary process for compensating fornon-ideal isotropic behavior of field probe, the field probe havingthree orthogonal sensors. The method includes, during a measurementprocedure, optionally positioning one of the field probe and a source ata set of incidence angles (θ, ϕ) (Block S124); measuring from thesensors an ordered triplet of field measurements, Ex(θ, ϕ), Ey(θ, ϕ) andEz(θ, ϕ) (Block S126); determining from a table a set of incident angles(θ′, ϕ′) corresponding to the field measurements (Block S128);determining from a table a correction factor corresponding to theincident angles (θ′, ϕ′) (Block S130); and multiplying the fieldmeasurements by the correction factor to obtain corrected measurements,Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ) (Block S132).

Thus, some embodiments include a method for compensating for non-idealisotropic behavior of a field probe. The method includes, during acalibration procedure, for each of a plurality of positions of the fieldprobe relative to a source, each position denoted by a set of angles (θ,ϕ), performing the following steps: measuring a field by a plurality ofsensors of the field probe, storing the measurements by the sensors andthe set of angles (θ, ϕ), computing a correction factor for the set ofangles (θ, ϕ) based on the measurements, and storing the correctionfactor. Thus, in some embodiments, during the calibration, a known fieldmay be applied and a set of corrections may be computed and stored.During measurement, from the probe readings, one can look up and findthe angle pair. Corrections can then be applied for that angledirection.

According to this aspect, in some embodiments, the field probe comprisesthree orthogonally-directed sensors and a measurement is made by eachsensor for each set of angles (θ, ϕ). In some embodiments, thecorrection factor is given by:

$\begin{matrix}{{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}},} & \;\end{matrix}$

where k is the correction factor for the set of angles (θ, ϕ), Ex, Eyand Ez are the fields measured by the three sensors as expressed in anx-y-z coordinate system, respectively, and E_(inc) is a magnitude of anapplied known field. In some embodiments, the fields Ex, Ey and Ez arenormalized prior to storing the measurement according to:(E_(x)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(y)/√{squareroot over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(z)/√{square root over (E_(x)²+E_(y) ²+E_(z) ²)}), respectively. In some embodiments, the field probecomprises six orthogonally-directed sensors and a measurement is made byeach sensor for each set of angles (θ, ϕ). In some embodiments, thefield probe has a plurality of sensors and measuring the field by thefield probe includes measuring by each sensor a field value that ismapped to three orthogonal directions. According to another aspect, amethod for compensating for non-ideal isotropic behavior of a fieldprobe is provided. The method includes, during a measurement procedure,measuring a field by a plurality of sensors of the field probe,determining an angle of incidence based on the measurement, determininga correction factor corresponding to the angle of incidence, andmultiplying the measured field by the correction factor to obtain acorrected measurement.

According to this aspect, in some embodiments, the measured field isnormalized prior to determining the angle of incidence. In someembodiments, the angle of incidence is determined from a table that mapsmeasurements to angles. In some embodiments, the correction factor isdetermined from a table that maps angles to correction factors. In someembodiments, the correction factor is determined from a table that mapsmeasurements to correction factors.

According to yet another aspect, FIG. 8 is a block diagram of acalibration and measurement correction processing circuitry 20, such asconfigured to calibrate and store measurements and correction factorsfor compensating for non-ideal isotropic behavior of a field probe isprovided. The apparatus includes, during a calibration procedure, acalibration processor 20-A which, for each of a plurality of positionsof the field probe relative to a source, each position denoted by a setof angles (θ, ϕ): obtains a measurement by each sensor via the fieldmeasurement collection unit 22; computing a correction factor, k(θ, ϕ)based on the measurements via a correction factor computer 24; andstoring via the field measurement collection unit 22 the measurements ofthe sensors, the set of angles corresponding to the measurement of thesensors and the correction factor k(θ, ϕ).

According to this aspect, in some embodiments, the correction factor isgiven by:

$\begin{matrix}{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}} & \;\end{matrix}$

wherein Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ) are the field measurementsderived from the sensor measurements at each position and set of angles(θ, ϕ). In some embodiments, the measured fields Ex(θ, ϕ), Ey(θ, ϕ) andEz(θ, ϕ) are normalized according to: (E_(x)/√{square root over (E_(x)²+E_(y) ²+E_(z) ²)}, E_(y)/√{square root over (E_(x) ²+E_(y) ²+E_(z)²)}, E_(z)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)}), respectively.

According to another aspect, an apparatus to generate correctedmeasurements from a field probe, the apparatus including processingcircuitry 20 configured to compensate for non-ideal isotropic behaviorof the field probe, the field probe having three orthogonal sensors. Theprocessing circuitry 20 is configured to, during a measurementprocedure: collect a set of measurements by the field probe via thefield measurement collection unit 26. determine, via the fieldmeasurement collection unit 26, from measurements by the sensors, anordered triplet of field measurements, Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ);determine, via an angle of incidence determiner 28, from a table a setof incident angles (θ′, ϕ′) corresponding to the field measurements;determine via a correction factor look up unit 30, which looks up acorrection factor from a table at a memory location corresponding to theincident angles (θ′, ϕ′); and multiply, via the measurement multiplier32, the field measurements by the correction factor to obtain correctedmeasurements, Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ).

According to this aspect, in some embodiments, the field measurementsare normalized prior to determining the incident angles. In someembodiments, the incident angles are determined from a table that mapsmeasurements to angles. In some embodiments, the correction factor isdetermined from a table that maps angles to correction factors.

It will be understood that the processing circuitry 20 can beimplemented as a computer processor and memory for computing and storingcorrection factors and corrected measurements. Alternatively, processingcircuitry 20 can be implemented as application specific circuitry or acombination of application specific circuitry and the computer processorand memory.

It will be understood that storing the measurement and the anglesassociated with that measurement may be accomplished by storing themeasurement in an addressable, searchable memory such that the memorymay be searched for angles that correspond to a measurement. It willalso be understood that storing the correction factors may beaccomplished by storing the correction factors in an addressablesearchable memory such that the memory may be addressed to retrieve acorrection factor corresponding to a set of angles. The steps of any ofthe methods set forth herein may be performed by a processor incommunication with such memory, the processor being application specificcircuitry or a programmable processor operating according to computerinstructions to cause the processor to perform the steps of such method.It will further be understood that although a probe may have threeorthogonal sensors and corrections may be determined for a pair ofangles defining a three dimensional space, the methods set forth hereinmay be applied to a probe having two orthogonal sensors and correctionsmay be determined for a pair of angles where one of the angles is fixed,defining a two dimensional space. It will be further understood that aprobe may have greater than three orthogonal sensors and corrections maybe determined for a pair of angles defining a three dimensional space.

Thus, a method, system and apparatus for compensating for non-idealisotropic behavior of a field probe are disclosed. A method includes,during a calibration procedure, for each of a plurality of positions ofthe field probe relative to a source, each position denoted by a set ofangles (θ, ϕ), performing the following steps: measuring a field by thesensors of the probe, storing the measurements and the set of angles (θ,ϕ) for each measurement, computing a correction factor for the set ofangles (θ, ϕ) based on the measurement, and storing the correctionfactors. During a measurement procedure, each sensor measures acomponent of the field. A set of angles is determined based on thesensor measurements, and a correction factor is determined based on theset of angles. The correction factor may then be multiplied by thesensor measurements to obtain the corrected field measurements.

Some embodiments include:

Embodiment A1

A method for compensating for non-ideal isotropic behavior of a fieldprobe, the method comprising:

-   -   during a calibration procedure:    -   rotating the field probe to a plurality of angles, and for each        angle, recording a reading of the field probe;    -   computing a correction factor for each angle based on the        reading for the angle; and storing the field probe readings, the        angles and the correction factors.

Embodiment A2

The method of Embodiment A1, wherein the field probe comprises threeorthogonally-directed probes and a field component reading for eachdirection of orientation is recorded and stored for each angle.

Embodiment A3

The method of Embodiment A2, wherein the correction factor is given by:

$\begin{matrix}{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}} & \;\end{matrix}$

where k is the correction factor for incident field angle (θ, ϕ), andE_(inc) is a magnitude of an applied field.

Embodiment B1

A method for compensating for non-ideal isotropic behavior of a fieldprobe, the method comprising:

-   -   during a measurement procedure:    -   measuring a field by the field probe;    -   using the measurement of the field to determine an angle of        incidence;    -   determining a correction factor corresponding to the angle of        incidence;    -   multiplying the measured field by the correction factor to        obtain a corrected measurement.

Embodiment B2

The method of Embodiment B1, wherein the measured field is normalizedprior to determining the angle of incidence.

Embodiment B3

The method of Embodiment B1, wherein the angle of incidence isdetermined from a table that maps measurements to angles.

Embodiment B4

The method of Embodiment B1, wherein the correction factor is determinedfrom a table that maps angles to correction factors.

As will be appreciated by one of skill in the art, the conceptsdescribed herein may be embodied as a method, data processing system,computer program product and/or computer storage media storing anexecutable computer program. Accordingly, the concepts described hereinmay take the form of an entirely hardware embodiment, an entirelysoftware embodiment or an embodiment combining software and hardwareaspects all generally referred to herein as a “circuit” or “module.” Anyprocess, step, action and/or functionality described herein may beperformed by, and/or associated to, a corresponding module, which may beimplemented in software and/or firmware and/or hardware. Furthermore,the disclosure may take the form of a computer program product on atangible computer usable storage medium having computer program codeembodied in the medium that can be executed by a computer. Any suitabletangible computer readable medium may be utilized including hard disks,CD-ROMs, electronic storage devices, optical storage devices, ormagnetic storage devices.

Some embodiments are described herein with reference to flowchartillustrations and/or block diagrams of methods, systems and computerprogram products. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer (to therebycreate a special purpose computer), special purpose computer, or otherprogrammable data processing apparatus to produce a machine, such thatthe instructions, which execute via the processor of the computer orother programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

These computer program instructions may also be stored in a computerreadable memory or storage medium that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer readablememory produce an article of manufacture including instruction meanswhich implement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

It is to be understood that the functions/acts noted in the blocks mayoccur out of the order noted in the operational illustrations. Forexample, two blocks shown in succession may in fact be executedsubstantially concurrently or the blocks may sometimes be executed inthe reverse order, depending upon the functionality/acts involved.Although some of the diagrams include arrows on communication paths toshow a primary direction of communication, it is to be understood thatcommunication may occur in the opposite direction to the depictedarrows.

Computer program code for carrying out operations of the conceptsdescribed herein may be written in an object oriented programminglanguage such as Java® or C++. However, the computer program code forcarrying out operations of the disclosure may also be written inconventional procedural programming languages, such as the “C”programming language. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer. In the latter scenario, theremote computer may be connected to the user's computer through a localarea network (LAN) or a wide area network (WAN), or the connection maybe made to an external computer (for example, through the Internet usingan Internet Service Provider).

Many different embodiments have been disclosed herein, in connectionwith the above description and the drawings. It will be understood thatit would be unduly repetitious and obfuscating to literally describe andillustrate every combination and subcombination of these embodiments.Accordingly, all embodiments can be combined in any way and/orcombination, and the present specification, including the drawings,shall be construed to constitute a complete written description of allcombinations and subcombinations of the embodiments described herein,and of the manner and process of making and using them, and shallsupport claims to any such combination or subcombination.

It will be appreciated by persons skilled in the art that theembodiments described herein are not limited to what has beenparticularly shown and described herein above. In addition, unlessmention was made above to the contrary, it should be noted that all ofthe accompanying drawings are not to scale. A variety of modificationsand variations are possible in light of the above teachings withoutdeparting from the scope of the following claims.

1. A method for compensating for non-ideal isotropic behavior of a fieldprobe, the method comprising: during a calibration procedure, for eachof a plurality of positions of the field probe relative to a source,each position denoted by a set of angles (θ, ϕ); measuring a field by aplurality of sensors of the field probe; storing the measurements by thesensors and the set of angles (θ, ϕ); computing a correction factor forthe set of angles (θ, ϕ) based on the measurements; and storing thecorrection factor.
 2. The method of claim 1, wherein the field probecomprises three orthogonally-directed sensors and a measurement is madeby each sensor for each set of angles (θ, ϕ).
 3. The method of claim 2,wherein the correction factor is given by: $\begin{matrix}\begin{matrix}{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}} & \;\end{matrix} & \;\end{matrix}$ where k is the correction factor for the set of angles (θ,ϕ), Ex, Ey and Ez are the fields measured by the three sensors asexpressed in an x-y-z coordinate system, respectively, and E_(inc) is amagnitude of an applied known field.
 4. The method of claim 3, whereinthe fields Ex, Ey and Ez are normalized prior to storing the measurementaccording to: (E_(x)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)},E_(y)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(z)/√{square rootover (E_(x) ²+E_(y) ²+E_(z) ²)}), respectively.
 5. The method of claim1, wherein the field probe comprises six orthogonally-directed sensorsand a measurement is made by each sensor for each set of angles (θ, ϕ).6. The method of claim 1, wherein the field probe has a plurality ofsensors and measuring the field by the field probe includes measuring byeach sensor a field value that is mapped to three orthogonal directions.7. A method for compensating for non-ideal isotropic behavior of a fieldprobe, the method comprising: during a measurement procedure: measuringa field by a plurality of sensors of the field probe; determining anangle of incidence based on the measurements; determining a correctionfactor corresponding to the angle of incidence; and multiplying themeasured field by the correction factor to obtain a correctedmeasurement.
 8. The method of claim 7, wherein the measured field isnormalized prior to determining the angle of incidence.
 9. The method ofclaim 7, wherein the angle of incidence is determined from a table thatmaps measurements to angles.
 10. The method of claim 7, wherein thecorrection factor is determined from a table that maps angles tocorrection factors.
 11. The method of claim 7, wherein the correctionfactor is determined from a table that maps measurements to correctionfactors.
 12. An apparatus configured to calibrate and store measurementsand correction factors, the apparatus comprising processing circuitryconfigured to: during a calibration procedure, for each of a pluralityof positions of the field probe relative to a source, each positiondenoted by a set of angles (θ, ϕ): obtain a measurement by each sensor;compute a correction factor, k(θ, ϕ) based on the measurements; andstore the measurements of the sensors, the set of angles correspondingto the measurements and the correction factor k(θ, ϕ).
 13. The apparatusof claim 12, wherein the correction factor is given by: $\begin{matrix}{{k\left( {\theta,\varphi} \right)} = \frac{E_{inc}}{{\sqrt{{E_{x}\left( {\theta,\varphi} \right)}^{2} + {E_{y}\left( {\theta,\varphi} \right)}^{2} + {E_{z}\left( {\theta,\varphi} \right)}^{2}}}_{}}} & \;\end{matrix}$ wherein Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ) are the fieldmeasurements derived from the sensor measurements at each position andset of angles (θ, ϕ).
 14. The apparatus of claim 13, wherein the fieldmeasurements Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ) are normalized accordingto: (E_(x)/√{square root over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(y)/√{squareroot over (E_(x) ²+E_(y) ²+E_(z) ²)}, E_(z)/√{square root over (E_(x)²+E_(y) ²+E_(z) ²)}), respectively.
 15. An apparatus configured togenerate corrected measurements, the apparatus comprising processingcircuitry configured to: during a measurement procedure: determine frommeasurements by the sensors, an ordered triplet of field measurements,Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ); determine from a table a set ofincident angles (θ′, ϕ′) corresponding to the field measurements;determine from a table a correction factor corresponding to the incidentangles (θ′, ϕ′) obtained from the table; and multiply the fieldmeasurements by the correction factor to obtain corrected measurements,Ex(θ, ϕ), Ey(θ, ϕ) and Ez(θ, ϕ).
 16. The apparatus of claim 15, whereinthe field measurements are normalized prior to determining the incidentangles.
 17. The apparatus of claim 15, wherein the incident angles aredetermined from a table that maps measurements to angles.
 18. Theapparatus of claim 15, wherein the correction factor is determined froma table that maps angles to correction factors.